PHOSP is a study aiming to investigate the long term effects of coronavirus on patients who were hospitalised with the disease. It will recruit 10,000 volunteers from the UK, and has stated that it intends to investigate:

the short (0-6 months), medium (6-12 months) and long term (12 months +) effects of the disease.

What fraction of hospitalised COVID-19 patients will still experience symptoms after 12 months?

This question will resolve according to a published estimate from PHOSP, of the fraction of hospitalised patients enrolled in the study who displayed symptoms 12+ months later. Symptoms may be of any sort considered clinically relevant by PHOSP. As a non-exhaustive example of what they are currently investigating, their about page states:

The range and severity of symptoms arising from the virus is broad, from those with no or minimal symptoms, to severe pneumonia in 15-20 per cent of cases, with evidence of widespread disease beyond the lungs, including the heart and circulatory system, kidney damage and effects on the brain.